Specific Force Calculator

At a glance:Specific force (also 'momentum function') is the core quantity for analysing hydraulic jumps and conjugate depths in open-channel hydraulics. It comes from momentum conservation: add the hydrostatic-pressure term and the momentum-flux term of a section (per unit width for a rectangular channel, divided by the fluid weight) to get the specific force M. For a rectangular channel, M=q²/(g·y)+y²/2, where M is specific force (m³/m), q unit discharge (m³/s per m), g=9.81 m/s², y depth (m). Term by term: q²/(g·y) is the momentum flux (inertia, large at shallow fast flow); y²/2 is the hydrostatic force of a unit-width triangular pressure distribution (large at deep flow). The two trade off, giving M a minimum at the critical depth yc (Fr=1). Key property: over a short horizontal reach ignoring bed friction, the specific force is equal before and after a jump (momentum conserved) — the two depths with equal M (one shallow, one deep, straddling critical) are the conjugate depths. From M(y₁)=M(y₂) you get the sequent depth y₂ (Belanger equation: y₂/y₁=½(√(1+8Fr₁²)−1)), and the specific-energy drop gives the jump loss. Example: q=2 m³/s/m, y=1 m → M=2²/(9.81×1)+1²/2=0.4078+0.5=0.9078 m³/m. Uses: (1) hydraulic-jump analysis — stilling-basin depth and energy dissipation; (2) jump location/strength downstream of gates and spillways; (3) locate critical flow (minimum M → yc); (4) momentum of varied open-channel flow. Notes: (1) this is the rectangular, unit-width form; non-rectangular sections differ (use area and centroid); (2) M is conserved only when bed slope and friction on the reach are negligible; (3) M has a minimum at critical depth — one M maps to two conjugate depths; (4) q is unit discharge (total ÷ width); (5) keep SI units. In short, specific force M=q²/(gy)+y²/2 is momentum plus hydrostatic pressure, and by M equal before/after a jump it finds conjugate depths — the basis of stilling-basin design.